Bi-Heyting algebras, toposes and modalities

Journal of Philosophical Logic 25 (1):25 - 43 (1996)
The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs
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DOI 10.1007/BF00357841
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A Topos-Theoretic Approach to Reference and Modality.Gonzalo E. Reyes - 1991 - Notre Dame Journal of Formal Logic 32 (3):359-391.
Doctrines in Categorical Logic.Anders Kock & Gonzalo E. Reyes - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 90.

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An Algebraic Approach to Intuitionistic Connectives.Xavier Caicedo & Roberto Cignoli - 2001 - Journal of Symbolic Logic 66 (4):1620-1636.

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